Recreation Studies—Pleasure Craft Purchasing: Suppose an investment firm is trying to dete...

Recreation Studies—Pleasure Craft Purchasing: Suppose an investment firm is trying to determine which type of recreational activity shows a high rate of growth so that it can make a profit on its investment. The amount Americans spent on boats and pleasure craft annually from 1990 to 2010 can be modeled by

where x represents the number of years since 1990, and f(x) represents the annual amount spent on boats and pleasure craft in billions of dollars. (Source: U.S. Bureau of Economic Analysis.)

(a) Determine f′(x).

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(b) Use part (a) to determine the rate at which the spending on boats and pleasure craft was increasing in 2008.